Score : $500$ points

Problem Statement

To decide which is the strongest among Rock, Paper, and Scissors, we will hold an RPS tournament. There are $2^k$ players in this tournament, numbered $0$ through $2^k-1$. Each player has his/her favorite hand, which he/she will use in every match.

A string $s$ of length $n$ consisting of R, P, and S represents the players' favorite hands. Specifically, the favorite hand of Player $i$ is represented by the $((i\text{ mod } n) + 1)$-th character of $s$; R, P, and S stand for Rock, Paper, and Scissors, respectively.

For $l$ and $r$ such that $r-l$ is a power of $2$, the winner of the tournament held among Players $l$ through $r-1$ will be determined as follows:

• If $r-l=1$ (that is, there is just one player), the winner is Player $l$.
• If $r-l\geq 2$, let $m=(l+r)/2$, and we hold two tournaments, one among Players $l$ through $m-1$ and the other among Players $m$ through $r-1$. Let $a$ and $b$ be the respective winners of these tournaments. $a$ and $b$ then play a match of rock paper scissors, and the winner of this match - or $a$ if the match is drawn - is the winner of the tournament held among Players $l$ through $r-1$.

Find the favorite hand of the winner of the tournament held among Players $0$ through $2^k-1$.

Notes

• $a\text{ mod } b$ denotes the remainder when $a$ is divided by $b$.
• The outcome of a match of rock paper scissors is determined as follows:- If both players choose the same hand, the match is drawn;
  • R beats S;
  • P beats R;
  • S beats P.
• If both players choose the same hand, the match is drawn;
• R beats S;
• P beats R;
• S beats P.

Constraints

• $1 \leq n,k \leq 100$
• $s$ is a string of length $n$ consisting of R, P, and S.

Input

Input is given from Standard Input in the following format:

$n$ $k$

$s$

Output

Print the favorite hand of the winner of the tournament held among Players $0$ through $2^k-1$, as R, P, or S.

3 2
RPS

P

• The favorite hand of the winner of the tournament held among Players $0$ through $1$ is P.
• The favorite hand of the winner of the tournament held among Players $2$ through $3$ is R.
• The favorite hand of the winner of the tournament held among Players $0$ through $3$ is P.

Thus, the answer is P.

P
 ┌─┴─┐
 P   R
┌┴┐ ┌┴┐
R P S R

11 1
RPSSPRSPPRS

P

1 100
S

S